Algebra was developed as a separate section of mathematics to solve problems involving unknown numbers. In algebra, unknown numbers are represented by variables like x, allowing problems to be solved using the same addition, subtraction, etc. operations as regular arithmetic. For example, if the number of boys in a class is unknown and represented by x, we can write an equation relating x to the total number of students and known number of girls to solve for x. Algebra introduces variables like x to represent unknowns, but applies the same basic math operations as used with numbers.

1. Algebra - Origin
Till now you dealt with mathematics involving numbers.
As we move further we have to deal with unknown numbers
Like for example: A father’s age is thrice the age of his Son. 10 years passed. Now
father’s age is double the age of his son. So what is the age of both at present?
As you can realize this problem can’t be solved mere using numbers. We have two
unknowns here. Age of father and age of son. We also have a number 10.
So to solve such type of problems involving unknown numbers a
separate section of mathematics was started.
That is ALGEBRA. Maths of unknowns
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2. Algebra
Mathematics
with ‘x’
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3. Algebra
Algebra is nothing but maths using ‘x’
‘x’ is nothing but a term used to denote something
unknown.
Till now we dealt with just numbers in mathematics.
In algebra along with numbers we use ‘x’ and do same
addition, subtraction etc
So algebra is nothing new kind of thing
.. don’t worry..We shall make it simple to you.. 
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4. Algebra
Now lets take one problem to understand
Assume a class has total of 60 students.
Out of them 25 are girls.
Now how many are boys?
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5. Algebra
Here number of boys is unknown.
So lets assume it as ‘x’ number of boys.
‘x’ is used for unknown terms
Now according to the given data total of
students is 60..
i.e. boys + girls is 60.
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6. Algebra
So now we have
x (boys) + 25 (girls) = 60
x(boys) = 60 – 25 (total – girls)
x (boys) = 35
So number of boys is 35…
This is how unknown ‘x’ is used
as you see rest is simple maths
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7. Algebra
If there are different types of unknowns terms
like different kind of bunch of fruits mangos,
bananas, oranges, apples.. are present.
Then we can use like ‘x’ number of mangos, ‘y’
number of bananas, ‘z’ oranges, ‘a’ apples ….
where x, y, z, a.. are unknown numbers
So we can use all alphabets for denoting
unknown numbers
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8. Algebra
Lets say we have some ‘x’ (unknown) number of
chocolates
Again we purchased same ‘x’ number of chocolates
so total of chocolates would x + x = 2x
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9. Algebra
Continuing with ‘2x’ chocolates, suppose we get ‘3x’
chocolates from another friend.
Total will be 2x+3x = 5x
Now we distributed ‘4x’ chocolates to all class mates.
Now balance chocolates left is 5x - 4x = 1x
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10. Algebra
So it is simple, right?
It is just that we have this new term ‘x’
Rest of the things are same.
Addition and Subtraction same as before.
However there are few new rules.
We shall see them in next class.
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11. Algebra - Summary
• Algebra is mathematics with ‘x’
• The ‘x’ is used for unknown numbers.
• All alphabets can be used for unknown
numbers in algebra.
• Addition and Subtraction in algebra is
similar and simple as in arithmetic.
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